A. Uribe‐sanchez

A multicriteria framework with voxel‐dependent parameters for radiotherapy treatment plan optimization

PURPOSE To establish a new mathematical framework for radiotherapy treatment optimization with voxel-dependent optimization parameters. METHODS In the treatment plan optimization problem for radiotherapy, a clinically acceptable plan is usually generated by an optimization process with weighting factors or reference doses adjusted for a set of the objective functions associated to the organs. Recent discoveries indicate that adjusting parameters associated with each voxel may lead to better plan quality. However, it is still unclear regarding the mathematical reasons behind it. Furthermore, questions about the objective function selection and parameter adjustment to assure Pareto optimality as well as the relationship between the optimal solutions obtained from the organ-based and voxel-based models remain unanswered. To answer these questions, the authors establish in this work a new mathematical framework equipped with two theorems. RESULTS The new framework clarifies the different consequences of adjusting organ-dependent and voxel-dependent parameters for the treatment plan optimization of radiation therapy, as well as the impact of using different objective functions on plan qualities and Pareto surfaces. The main discoveries are threefold: (1) While in the organ-based model the selection of the objective function has an impact on the quality of the optimized plans, this is no longer an issue for the voxel-based model since the Pareto surface is independent of the objective function selection and the entire Pareto surface could be generated as long as the objective function satisfies certain mathematical conditions; (2) All Pareto solutions generated by the organ-based model with different objective functions are parts of a unique Pareto surface generated by the voxel-based model with any appropriate objective function; (3) A much larger Pareto surface is explored by adjusting voxel-dependent parameters than by adjusting organ-dependent parameters, possibly allowing for the generation of plans with better trade-offs among different clinical objectives. CONCLUSIONS The authors have developed a mathematical framework for radiotherapy treatment optimization using voxel-based parameters. The authors can improve the plan quality by adjusting voxel-based weighting factors and exploring the unique and large Pareto surface which include all the Pareto surfaces that can be generated by organ-based model using different objective functions.

TU‐G‐BRB‐07: Improve PTV Dose Distribution by Using Spatial Information in IMRT Optimization

Purpose: The spatial distribution of radiation dose within the PTV does have clinical significance. For instance, if hot/cold spots in the PTV cannot be avoided, high doses are preferred to be located in the center, and low doses at the peripheries. However, traditional plan optimization models for IMRT usually treat equally voxels inside the same structure, failing to incorporate those location preferences. We present a re‐optimization model that, while preserving the quality of an initial treatment plan represented by DVH curves, incorporates spatial information for voxels inside the PTV into the optimization to generate a more desirable dose distribution. Methods: Our re‐optimization model incorporates a convex function that penalizes the deviation of the dose received by each voxel from an individual reference value. For PTV, the reference values per voxel match the ideal redistribution of the initial PTV dose, where voxels close to the boundary receive the low doses, while voxels in the center receive the high doses. For OAR, the reference value per voxel corresponds to its dose from the initial plan. In addition to the structure‐based weighting factors in traditional planning approaches, we incorporated individual penalty weights for PTV voxels. Structure‐based factors are calibrated according to the difference from the reference DVH curves, while voxel‐based, according to the difference to reference value. Results: We tested our model in four gynecologic cancer cases. For each case, we compare the resulting dose distribution within the PTV to that from the initial plan. It is observed that without sacrificing the plan quality represented by DVH curves, our re‐optimization model generates more desirable PTV dose distributions. Conclusions: We have presented a re‐optimization model that, by incorporating spatial location information for PTV voxels, yields to more clinically favorable dose distributions with similar DVH curves. This work is supported by Varian Medical Systems through a Master Research Agreement.

TU-G-BRB-09: A Bregman Iteration Method for IMRT Optimization with Dose-Volume Histogram Constraints

Purpose:Dose‐volume histogram (DVH) is a clinically relevant criterion to evaluate treatment plan quality. It is hence desirable to incorporate the associated DVH constraints in treatment plan optimization. Yet, these constraints usually lead to difficulties due to their non‐convex nature. This project develops an algorithm to solve the intensity modulated radiation therapy(IMRT)optimization problem with DVH constraints considered via a Bregman iteration. Methods: We consider an objective function of a quadratic form with different overdose and underdose penalties, subject to DVH constraints. The constrained optimization problem is converted into a sequence of unconstrained problems via Bregman iteration approach, which are then solved sequentially using gradient‐descent algorithm with inexact line search. The objective functions in those unconstrained optimization problems contains terms that requires the computation of DVH values. In practice, this is achieved by approximating the Heaviside step‐functions in the expression of a DVH curve by a smoothed arctangent function. This approach also allows for the computation of gradient of the objective functions during optimization process. Results: We have tested our algorithm in the context of 7‐field IMRTtreatment planning for prostate cancer in 4 patient cases. Clinically relevant DVH constraints are considered for PTV, rectum, and bladder. In all the cases, the algorithm is able to find the solutions that satisfy all the DVH constraints, while as DVH constraints may be violated when the Bregman algorithm is not applied. The local‐minima problem caused by the non‐convex constraints is not observed, which may be ascribed to the good quality of the initial dose distribution obtained after a standard IMRToptimization problem without DVH constraints. Conclusions: We have developed an algorithm to solve the IMRToptimization problem with DVH constraints using Bregman iteration approach. Tests conducted in prostate cancer cases have demonstrated the validity of our algorithm and its effectiveness.

TU‐G‐BRB‐08: IMRT Optimization with Fixed Point Iteration

Purpose: In IMRToptimization, dose‐deposition coefficient (DDC) matrix is needed to parameterize the contribution of each beamlet to each dose voxel. However, due to the limitation of computer memory and the requirement on computational efficiency, small matrix elements are usually truncated, compromising the resulting plans quality. Besides, the practice of ignoring multileaf collimator(MLC) transmission in IMRT planning also introduces inaccuracy into the resulting plan. Therefore an IMRToptimization algorithm with fixed point iteration is developed. Methods: For truncation problem, IMRToptimization is implemented as the inner‐loop with truncated DDC matrix. Fixed point iteration, as the outer‐loop, is to recalculate the actual dose with complete DDC matrix and use the difference between the optimized dose and the actual dose as the input for the optimization at the next iteration. MLC transmission can also be incorporated into IMRT planning, by adding this fixed point iteration to optimize the intensity of the already optimized apertures. The convergence and feasibility of this algorithm are mathematically studied using a simplified model. Results: Two head‐and‐neck IMRT cases are used to test our algorithm. It is mathematically proven and experimentally validated on the simplified model that with proper DDC matrix splitting, the fixed point iteration converges, although not to the solution obtained using the complete DDC matrix, but to a solution much closer to it than that from the truncated DDC matrix, in terms of the resulting dose distribution. The experimental results on the patient cases also demonstrate that our algorithm could handle both DDC matrix truncation and MLC transmission problems and give us good plans with comparable dose‐volume histograms and dose distributions. Conclusions: This fixed point iteration scheme can effectively take the DDC matrix truncation and MLC transmission into account during IMRToptimization, and thus solve the efficiency and memory issue while maintaining a reasonable accuracy. This work is supported by Varian Medical Systems through a Master Research Agreement.

SU‐E‐T‐503: IMRT Optimization Using Monte Carlo Dose Engine: The Effect of Statistical Uncertainty

PURPOSE With the development of ultra-fast GPU-based Monte Carlo (MC) dose engine, it becomes clinically realistic to compute the dose-deposition coefficients (DDC) for IMRT optimization using MC simulation. However, it is still time-consuming if we want to compute DDC with small statistical uncertainty. This work studies the effects of the statistical error in DDC matrix on IMRT optimization. METHODS The MC-computed DDC matrices are simulated here by adding statistical uncertainties at a desired level to the ones generated with a finite-size pencil beam algorithm. A statistical uncertainty model for MC dose calculation is employed. We adopt a penalty-based quadratic optimization model and gradient descent method to optimize fluence map and then recalculate the corresponding actual dose distribution using the noise-free DDC matrix. The impacts of DDC noise are assessed in terms of the deviation of the resulted dose distributions. We have also used a stochastic perturbation theory to theoretically estimate the statistical errors of dose distributions on a simplified optimization model. RESULTS A head-and-neck case is used to investigate the perturbation to IMRT plan due to MCs statistical uncertainty. The relative errors of the final dose distributions of the optimized IMRT are found to be much smaller than those in the DDC matrix, which is consistent with our theoretical estimation. When history number is decreased from 108 to 106, the dose-volume-histograms are still very similar to the error-free DVHs while the error in DDC is about 3.8%. CONCLUSIONS The results illustrate that the statistical errors in the DDC matrix have a relatively small effect on IMRT optimization in dose domain. This indicates we can use relatively small number of histories to obtain the DDC matrix with MC simulation within a reasonable amount of time, without considerably compromising the accuracy of the optimized treatment plan. This work is supported by Varian Medical Systems through a Master Research Agreement.

TU‐G‐BRB‐02: A New Mathematical Framework for IMRT Inverse Planning with Voxel‐Dependent Optimization Parameters

PURPOSE To establish a new mathematical framework for IMRT treatment optimization with voxel-dependent optimization parameters. METHODS In IMRT inverse treatment planning, a physician seeks for a plan to deliver a prescribed dose to the target while sparing the nearby healthy tissues. The conflict between these objectives makes the multi-criteria optimization an appropriate tool. Traditionally, a clinically acceptable plan can be generated by fine-tuning organ-based parameters. We establish a new mathematical framework by using voxel-based parameters for optimization. We introduce three different Pareto surfaces, prove the relationship between those surfaces, and compare voxel-based and organ-based methods. We prove some new theorems providing conditions under which the Pareto optimality is guaranteed. RESULTS The new mathematical framework has shown that: 1) Using an increasing voxel penalty function with an increasing derivative, in particular the popular power function, it is possible to explore the entire Pareto surface by changing voxel-based weighting factors, which increases the chances of getting more desirable plan. 2) The Pareto optimality is always guaranteed by adjusting voxel-based weighting factors. 3) If the plan is initially produced by adjusting organ-based weighting factors, it is impossible to improve all the DVH curves at the same time by adjusting voxel-based weighting factors. 4) A larger Pareto surface is explored by changing voxel-based weighting factors than by changing organ-based weighting factors, possibly leading to a plan with better trade-offs. 5) The Pareto optimality is not necessarily guaranteed while we are adjusting the voxel reference doses, and hence, adjusting voxel-based weighting factors is preferred in terms of preserving the Pareto optimality. CONCLUSIONS We have developed a mathematical framework for IMRT optimization using voxel-based parameters. We can improve the plan quality by adjusting voxel-based weighting factors after organ-based parameter adjustment. This work is supported by Varian Medical Systems through a Master Research Agreement.

WE‐G‐BRCD‐01: A Procedure for Efficient Large‐Scale Retrospective Clinical Studies for Online Adaptive Radiotherapy

PURPOSE Online adaptive radiotherapy (ART) is promising for handling inter-fraction variations of patients geometry. Before a clinical implementation of this advanced technology, it is necessary to study its potential clinical gains and optimal frequencies to be used for various tumor sites. The goal of this work is to establish and examine a procedure for efficient large-scale retrospective clinical studies for online ART using a GPU-based re-planning platform. METHODS The proposed procedure utilizes an in-house developed GPU-based replanning software called SCORE. SCORE starts by applying deformable registration from CT to CBCT and correcting CBCT artifacts and intensities. However, the CBCT image may not cover the whole treatment region due to the limited field of view. In that case, we use deformed CT for replanning and dose calculation. The final optimized fractional dose is calculated using the optimized fluence maps and a finite size pencil beam model. We also use the deformed CT to calculate the delivered fractional dose using the fluence maps from the original plan. The delivered fractional dose is compared to the optimized fractional dose to estimate the daily gain of replanning. To compare accumulated optimized dose and delivered dose, the delivered and optimized doses are mapped back to the original CT geometry using the deformation vector fields. RESULTS We tested this procedure using prostate cancer IMRT cases and found that the re-optimized and delivered DVHs and dose distributions can be generated in a couple of minutes. CONCLUSIONS We have developed a procedure using a GPU-based replanning software to retrospectively study the clinical gains of online ART in an efficient and large scale manner.

SU‐E‐T‐805: A GPU‐Based Re‐Planning System for Online Adaptive Radiotherapy

Purpose: To develop a re‐planning platform based on Graphics Processing Unit (GPU). Methods: Our project is based on the Qt framework to build a multi‐platforms GUI and allowing the user to have a control on every step of the process. The GUI is designed to be extended each time a feature is needed. Into this GUI, we have integrated several different modules for each part of the workflow. We have modules for DICOM file handling, image pre‐processing, including structure identification from the contours, automatic rigid registration, CT to Cone Beam CT structure propagation and manual structure alignment. We also have modules for deformable image registration based on the demons algorithm, dose calculation and plan re‐optimization. Most of the modules have been implemented on a GPU to allow high efficiency treatment re‐planning. Also each module comes with a visualization tool to always have control of the entire procedure. Results: We have developed a Qt‐based GUI for online ART. GPU modules for image pre‐processing, deformable registration, dose calculation and plan optimization have been integrated within this GUI. Conclusions: We transformed stand‐alone efficient processing tools into a user‐friendly platform, that can be used by clinicians, in order to have a fast treatment re‐planning, and an overview of the results for plan inspection and approval.

TU‐A‐BRB‐08: Incorporation of Spatial Information into IMRT Plan Optimization

Purpose: In plan optimization of intensity‐modulated radiation therapy(IMRT), all voxels inside the same structure are treated equally. In realty, the spatial location of hot/cold spots does have some clinical. One example is that hot spots, if cannot be removed, are more preferred to be located at the center, rather than the edge, of the tumor. Our goal is to develop a method that while preserving the plan quality represented by the DVH curves, reallocates hot and cold spots to more clinically preferred locations, by incorporating voxels spatial information into the optimizationmodel. Methods and Materials: In traditional optimizationmodels, usually a convex objective function penalizes the deviation of the dose received by each voxel from its prescribed (if it is part of the target) or threshold dose (if it is part of a critical structure). In our model, instead of assuming an equal weight for all voxels inside a structure, we associate weights as a function of their physical position in the structure. By this modification, our model incorporates voxel‐based penalty weights for overdosing (penalizing the presence of hot spots) and underdosing (penalizing the presence of cold spots) depending of the location in the structure. The resulting convex optimization problem is solved by implementing a gradient algorithm with Armijo search. Results: We tested our model in four prostate cancer cases and we compare the characteristics of resulting hot/cold spots to those resulting from a correspondingly model without incorporating spatial information. It is observed that without sacrificing the plan quality represented by the DVH curves, our model relocates the hot/cold spots to more desired positions. Conclusions: We have proposed a new optimizationmodel that, by incorporating voxels spatial location information, generates similar DVH curves to those from traditional model, while capable of redistributing hot/cold spots to more desirable locations.

TH‐C‐BRA‐01: Online Adaptive Radiotherapy: Technical Barriers and Potential Solutions

By seamlessly integrating treatment simulation and planning into the treatment delivery process, online adaptive radiotherapy (ART) allows realtime treatment adaptations based on the current patient anatomy and therefore holds significant promise in maximally compensating for anatomical uncertainties. This new paradigm of cancerradiotherapy provides an opportunity to significantly reduce normal tissue toxicity and/or to improve tumor control. Additionally, online ART can also handle the interfraction variation of the organ motion pattern, the inaccuracy of patient positioning (fast but less accurate patient positioning is then allowed), direct treatment without a traditional CT simulation, and the change of treatment strategy in the middle of the treatment course. However, the clinical realization of online ART is extremely challenging, mainly due to three major barriers: the inability for real‐time treatment re‐planning, the concern of excessive imagingdose from daily CT/CBCT, and the lack of an efficient clinical workflow. To overcome these barriers, we have been developing a series of GPU‐based computational tools for real‐time re‐planning, GPU‐based low‐dose CT/CBCT reconstruction, and an innovative computational infrastructure for a streamlined clinical workflow. In this talk, we will discuss the current status of this effort and some initial clinical applications. This lecture will provide an overview of the technical barriers for the clinical realization of online adaptive radiotherapy as well as the current efforts to overcome these barriers. Learning Objectives: 1. Understand the great potential of online adaptive radiotherapy; 2. Understand the major technical barriers for the clinical realization of online adaptive radiotherapy; 3. Understand the great potential of using graphics processing unit (GPU) to achieve high computational efficiency; 4. Understand an IMRT plan can be developed in seconds using GPU‐ based computational tools; 5. Understand CT/CBCT imagingdose can be reduced by 1–2 orders of magnitude using new reconstruction algorithms; 6. Understand a streamlined clinical workflow can be developed for online adaptive radiotherapy.